Complexiton and resonant multiple wave solutions to the (2+1)-dimensional Konopelchenko–Dubrovsky equation

作者: Pinxia Wu , Yufeng Zhang , Iqbal Muhammad , Qiqi Yin

DOI: 10.1016/J.CAMWA.2018.05.024

关键词: Bilinear formAction (physics)SolitonType (model theory)One-dimensional spaceExponential functionMathematicsMathematical analysisSuperposition principleDirect method

摘要: Abstract In this paper, the (2+1)-dimensional Konopelchenko–Dubrovsky (KD) equation is investigated. Using Hirota direct method and linear superposition principle, complexiton resonant multiple wave solutions are successfully constructed. For method, it essential that finding bilinear form to KD applying its 2 N -soliton formulation in real field build -complexiton under action of pairs conjugate variables. The exponential traveling waves can generate solutions, then generalize principle complex field, we obtain some new type solutions. phenomena complexiton, presented by figures.

参考文章(46)
Wen-Xiu Ma, Lump solutions to the Kadomtsev–Petviashvili equation Physics Letters A. ,vol. 379, pp. 1975- 1978 ,(2015) , 10.1016/J.PHYSLETA.2015.06.061
Jon Nimmo, Claire Gilson, 良吾 広田, 敦 永井, The direct method in soliton theory ,(2004)
S Novikov, Sergei V Manakov, Lev Petrovich Pitaevskii, Vladimir Evgenevič Zakharov, Theory of Solitons: The Inverse Scattering Method ,(1984)
Yang Wang, Long Wei, New exact solutions to the ( 2+1) -dimensional Konopelchenko–Dubrovsky equation Communications in Nonlinear Science and Numerical Simulation. ,vol. 15, pp. 216- 224 ,(2010) , 10.1016/J.CNSNS.2009.03.013
Wen-Xiu Ma, Yuncheng You, Solving the Korteweg-de Vries equation by its bilinear form: Wronskian solutions Transactions of the American Mathematical Society. ,vol. 357, pp. 1753- 1778 ,(2004) , 10.1090/S0002-9947-04-03726-2
Wen Xiu Ma, Complexiton solutions to the Korteweg–de Vries equation Physics Letters A. ,vol. 301, pp. 35- 44 ,(2002) , 10.1016/S0375-9601(02)00971-4
B.G. Konopelchenko, V.G. Dubrovsky, Some new integrable nonlinear evolution equations in 2 + 1 dimensions Physics Letters A. ,vol. 102, pp. 15- 17 ,(1984) , 10.1016/0375-9601(84)90442-0
Abdul-Majid Wazwaz, The tanh method for traveling wave solutions of nonlinear equations Applied Mathematics and Computation. ,vol. 154, pp. 713- 723 ,(2004) , 10.1016/S0096-3003(03)00745-8